In this talk we summarize two recent efforts towards improving the theoretical predictions for the differential cross sections in top quark pair production. Both are related to the effect of soft gluons. The first result is the analytic calculation of the NNLO massive soft function which is an important ingredient in the resummation of threshold logarithms. The second is the matched NNLO+NNLL$'$ predictions which combine state-of-the-art NNLO QCD calculations with double resummation at NNLL$'$ accuracy of threshold logarithms arising from soft gluon emissions and of small mass logarithms.